Temperature-dependent stress-strain prediction model, model construction method and prediction method of high-temperature reinforced multiscale fiber hybrid polymer concrete

Abstract

This invention discloses a temperature-related stress-strain prediction model, construction method, and prediction method for high-temperature reinforced multi-scale fiber-reinforced hybrid geopolymer concrete. The model includes a compressive strength prediction model, a peak strain prediction model, an elastic modulus prediction model, and a stress-strain curve generation model based on rational fractional piecewise functions. Based on room-temperature mechanical parameters and a target calcination temperature, it can output the high-temperature compressive strength, peak strain, elastic modulus, and complete stress-strain curves across the entire temperature range from room temperature to 1000℃. Each sub-model is constructed through piecewise regression or polynomial regression, with prediction errors controlled within ±15%. This invention achieves quantitative characterization of the mechanical behavior of multi-scale fiber-reinforced hybrid geopolymer concrete under high-temperature conditions, providing a reliable theoretical basis for its performance design and application in high-temperature engineering.

Description

Technical Field

[0001] This invention relates to the field of concrete materials technology, specifically to a temperature-related stress-strain prediction model, model construction method, and prediction method for high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete. Background Technology

[0002] With increasingly stringent global demands for environmental sustainability, the construction industry's responsibility for carbon reduction as a key carbon emission source is becoming increasingly prominent. Statistics show that approximately 8% of global carbon emissions originate from the traditional cement concrete production process. Against this backdrop, geopolymers, prepared using industrial byproducts or natural aluminosilicate materials as precursors, have become promising green building materials due to their low energy consumption and low CO2 emissions. Geopolymers possess excellent mechanical and durability properties, and compared to traditional cement-based composites, they often exhibit superior high-temperature resistance. The compressive strength of ordinary cement concrete drops sharply at high temperatures, even posing a risk of cracking, while geopolymers can be further densified through sintering reactions in high-temperature environments, thus maintaining high residual strength.

[0003] Geopolymer materials are inherently brittle and lack crack resistance, which limits their application in structures requiring impact or seismic resistance. By incorporating refractory aggregates and multi-scale hybrid fiber systems, the toughness of the material can be synergistically improved, crack propagation can be inhibited, and its structural integrity and residual load-bearing capacity after high temperatures can be further enhanced.

[0004] Current research on fiber-reinforced geopolymers largely focuses on performance testing at single temperature points. Particularly for multi-scale hybrid fiber-reinforced systems, a comprehensive stress-strain curve prediction model spanning the entire temperature range from room temperature to high temperatures has not yet been established. Furthermore, the residual mechanical properties of high-temperature reinforced geopolymer concrete are significantly higher at high temperatures than at room temperature, and existing prediction formulas cannot accurately predict its mechanical properties at different temperatures. This makes it impossible to accurately assess the evolution of the mechanical behavior of high-temperature reinforced hybrid fiber-reinforced geopolymer concrete in real-world temperature variations during engineering design, severely limiting the reliable application of this material in high-temperature engineering. Summary of the Invention

[0005] Current technologies lack predictive models for the mechanical behavior of high-temperature reinforced multi-scale fiber-reinforced geopolymers at different temperature ranges. This invention proposes a temperature-related stress-strain prediction model for high-temperature reinforced multi-scale fiber-reinforced geopolymer concrete, along with a model construction method and prediction method. By establishing a temperature-related prediction model, this invention enables quantitative characterization of the stress-strain curves of high-temperature reinforced multi-scale fiber-reinforced geopolymer concrete at different temperature ranges, providing key theoretical basis and technical support for the performance design of this type of material in high-temperature environments.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: In a first aspect, the present invention provides a temperature-related stress-strain prediction model for high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete, comprising: The compressive strength prediction model is used to output the predicted compressive strength after high temperature at the target calcination temperature T. s c,T ; The peak strain prediction model is used to output the predicted peak strain value after high temperature at the target calcination temperature T. e c,T ; The elastic modulus prediction model is used to output the predicted elastic modulus value after high temperature at the target calcination temperature T. E 0,T ; Stress-strain full curve generation model, used to generate predicted values s c,T , e c,T and E 0,T The stress-strain curve at the target calcination temperature T is generated by using a rational fractional piecewise function.

[0007] As a further optimization of the present invention, the compressive strength prediction model adopts the following form: ; in: s c Compressive strength at room temperature; , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the target calcination temperature T; a, b, and c are fitting parameters.

[0008] As a further optimization of the present invention, the peak strain prediction model adopts the following form: ; in: e c Peak strain at room temperature; , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the target calcination temperature T.

[0009] As a further optimization of the present invention, the elastic modulus prediction model adopts the following form: ; in: E 0 The elastic modulus at room temperature; , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the target calcination temperature T.

[0010] As a further optimization of the present invention, the stress-strain full curve generation model adopts the following form: ; Where: is the stress value; is the strain value; , which is a parameter describing the shape of the rising segment of the curve; The fitting coefficients are denoted as .

[0011] As a further optimization of the present invention, the multi-scale fiber-hybrid geopolymer concrete comprises a geopolymer precursor, refractory aggregate, alkali activator, water, and multi-scale hybrid fibers; the multi-scale hybrid fibers comprise at least two of wollastonite fibers, basalt fibers, and steel fibers; the geopolymer precursor comprises fly ash and / or metakaolin; and the refractory aggregate is ceramic aggregate.

[0012] Secondly, the present invention provides a method for constructing the temperature-related stress-strain prediction model, comprising the following steps: Multiple sets of high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete specimens were prepared, and their compressive strength, peak strain, and elastic modulus were tested at room temperature and at several high-temperature target calcination temperatures. Based on the performance at room temperature, the compressive strength, peak strain and elastic modulus at the calcination temperature of each high-temperature target were normalized. Regression analysis was performed on the normalized compressive strength data and temperature to construct a compressive strength prediction model; Regression analysis was performed on the normalized peak strain data and temperature to construct a peak strain prediction model. Regression analysis was performed on the normalized elastic modulus data and temperature to construct an elastic modulus prediction model. Based on the output parameters of the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model, and combined with rational fractional piecewise functions, a temperature-related stress-strain full curve generation model is constructed.

[0013] Thirdly, this invention provides a method for predicting the high-temperature mechanical properties of high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete, employing the aforementioned temperature-related stress-strain prediction model, and including the following steps: Obtain the ambient temperature axial compressive mechanical parameters of the geopolymer concrete to be predicted, including its ambient temperature compressive strength. s c Peak strain at room temperature e c and room temperature elastic modulus E 0 ; By calling the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model, and inputting the target calcination temperature T and room temperature axial compressive parameters, the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model are obtained respectively. s c,T , e c,T and E 0,T ; Call the stress-strain full curve generation model and input... s c,T , e c,T and E 0,T Generate the full stress-strain curve at the target calcination temperature T; The output shows the predicted results of compressive strength, peak strain, elastic modulus, and stress-strain curve at the target calcination temperature T.

[0014] As a further optimization of the present invention, the prediction model covers the entire temperature range from room temperature to 1000℃, and the relative error of the prediction results is controlled within ±15%.

[0015] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the function of the temperature-related stress-strain prediction model, or implements the steps of the construction method, or implements the steps of the prediction method.

[0016] The temperature-related stress-strain prediction model, model construction method, and prediction method for high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete proposed in this invention achieve multiple beneficial effects: 1. The temperature-related stress-strain prediction model provided by this invention is the first to achieve quantitative characterization of the stress-strain curve of high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete in the entire temperature range from room temperature to 1000℃, and can continuously output the mechanical response at different calcination temperatures.

[0017] 2. The model of this invention integrates a compressive strength prediction model, a peak strain prediction model, an elastic modulus prediction model, and a stress-strain curve generation model. Based on the room-temperature axial compressive parameters and the target temperature T, it can simultaneously predict the compressive strength, peak strain, elastic modulus, and complete stress-strain curve after high temperature, providing comprehensive data support for engineering evaluation.

[0018] 3. This invention constructs sub-models through regression analysis and generates a full curve by combining rational fractional piecewise functions, thus controlling the relative error between the model predictions and measured values ​​within ±15%. This provides a reliable quantitative basis for the structural design and performance evaluation of high-temperature reinforced geopolymer concrete in high-temperature environments.

[0019] 4. This invention not only provides a specific predictive model form, but also clarifies the complete construction method from specimen preparation, performance testing, normalization processing to regression modeling, as well as the standardized prediction process from inputting room temperature parameters to outputting prediction results. This facilitates the replication, verification, and application of the model by those skilled in the art, and has clear operability and promotional value. Attached Figure Description

[0020] Figure 1 This is a comparison chart of the test values ​​and predicted values ​​of compressive strength for each embodiment from the room temperature range to the high temperature range of 1000℃.

[0021] Figure 2 This is a comparison chart of the peak strain test values ​​and predicted values ​​for each embodiment from the room temperature range to the high temperature range of 1000℃.

[0022] Figure 3 This is a comparison chart of the measured and predicted elastic modulus values ​​for each embodiment from the room temperature range to the high temperature range of 1000°C.

[0023] Figure 4 This is a comparison chart of the test values ​​and predicted values ​​of the stress-strain curves for each embodiment, from the room temperature range to the high temperature range of 1000℃. Detailed Implementation

[0024] The embodiments of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0025] Various modifications and variations can be made to this application without departing from its spirit or scope, which will be apparent to those skilled in the art. Therefore, this application is intended to cover modifications and variations falling within the scope of the corresponding claims (the claimed technical solutions) and their equivalents. It should be noted that the implementation methods provided in the embodiments of this application can be combined with each other without contradiction.

[0026] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] As described in the background section, designing and fabricating a temperature-related stress-strain prediction model, model construction method, and prediction method for high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete is of great research significance.

[0028] Example 1 In this example, the raw material components and contents of the geopolymer mortar, by mass parts, are as follows: 184 parts fly ash, 428 parts metakaolin, 1221 parts ceramic aggregate, 236 parts alkali activator, 112 parts water, 31 parts wollastonite fiber, and 79 parts steel fiber.

[0029] The prepared geopolymer cement paste has a 90-day compressive strength of 56.8 MPa at room temperature.

[0030] The prepared geopolymer pulp has a compressive strength of 55.3 MPa after being heated to 200℃.

[0031] The prepared geopolymer pulp has a compressive strength of 55.7 MPa after being heated to 400℃.

[0032] The prepared geopolymer pulp has a compressive strength of 54.6 MPa after being heated to 600℃.

[0033] The prepared geopolymer pulp has a compressive strength of 57.8 MPa after being heated to 800℃.

[0034] The prepared geopolymer pulp has a compressive strength of 83.4 MPa after being heated to 1000℃.

[0035] In the example s c,T / s c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0036] In the example e c,T / e c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the calcination temperature.

[0037] In the example E 0,T / E 0 The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0038] Example of a geopolymer stress-strain model: in , which is a parameter describing the shape of the rising segment of the curve. These represent the compressive strength, peak strain, and elastic modulus of the geopolymer after high temperature. The fitting coefficients are denoted as .

[0039] Table 1 In Example 1 Value table Table 2 In Example 1 Value table Example 2 In this example, the raw material components and contents of the geopolymer mortar, by mass parts, are as follows: 184 parts fly ash, 428 parts metakaolin, 1221 parts ceramic aggregate, 236 parts alkali activator, 112 parts water, 31 parts wollastonite fiber, and 118 parts steel fiber.

[0040] The prepared geopolymer cement paste has a 90-day compressive strength of 49.2 MPa at room temperature.

[0041] The prepared geopolymer pulp has a compressive strength of 50.4 MPa after being heated to 200℃.

[0042] The prepared geopolymer pulp has a compressive strength of 52.9 MPa after being heated to 400℃.

[0043] The prepared geopolymer pulp has a compressive strength of 52.7 MPa after being heated to 600℃.

[0044] The prepared geopolymer pulp has a compressive strength of 55.8 MPa after being heated to 800℃.

[0045] The prepared geopolymer pulp has a compressive strength of 66.0 MPa after being heated to 1000℃.

[0046] In the example s c,T / s c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0047] In the example e c,T / e c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the calcination temperature.

[0048] In the example E 0,T / E 0 The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0049] Example of a geopolymer stress-strain model: in , which is a parameter describing the shape of the rising segment of the curve. These represent the compressive strength, peak strain, and elastic modulus of the geopolymer after high temperature. The fitting coefficients are denoted as .

[0050] Table 3 In Example 2 Value table Table 4 In Example 2 Value table Example 3 In this example, the raw material components and contents of the geopolymer mortar, by mass parts, are as follows: 184 parts fly ash, 428 parts metakaolin, 1221 parts ceramic aggregate, 236 parts alkali activator, 112 parts water, 31 parts wollastonite fiber, 5 parts basalt fiber, and 79 parts steel fiber.

[0051] The prepared geopolymer cement paste has a 90-day compressive strength of 46.5 MPa at room temperature.

[0052] The compressive strength of the prepared geopolymer pulp after being heated to 200℃ is 49.6MPa.

[0053] The prepared geopolymer pulp has a compressive strength of 53.4 MPa after being heated to 400℃.

[0054] The prepared geopolymer pulp has a compressive strength of 54.6 MPa after being heated to 600℃.

[0055] The compressive strength of the prepared geopolymer pulp after high temperature of 800℃ is 66.2MPa.

[0056] The prepared geopolymer pulp has a compressive strength of 97.3 MPa after being heated to 1000℃.

[0057] In the example s c,T / s c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0058] In the example e c,T / e c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the calcination temperature.

[0059] In the example E 0,T / E 0 The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0060] Example of a geopolymer stress-strain model: in , which is a parameter describing the shape of the rising segment of the curve. These represent the compressive strength, peak strain, and elastic modulus of the geopolymer after high temperature. The fitting coefficients are denoted as .

[0061] Table 5 In Example 3 Value table Table 6 In Example 3 Value table Example 4 In this example, the raw material components and contents of the geopolymer mortar, by mass parts, are as follows: 184 parts fly ash, 428 parts metakaolin, 1221 parts ceramic aggregate, 236 parts alkali activator, 112 parts water, 31 parts wollastonite fiber, 11 parts basalt fiber, and 79 parts steel fiber.

[0062] The prepared geopolymer cement paste has a 90-day compressive strength of 48.2 MPa at room temperature.

[0063] The prepared geopolymer pulp has a compressive strength of 50.8 MPa after being heated to 200℃.

[0064] The prepared geopolymer pulp has a compressive strength of 54.4 MPa after being heated to 400℃.

[0065] The prepared geopolymer pulp has a compressive strength of 56.5 MPa after being heated to 600℃.

[0066] The prepared geopolymer pulp has a compressive strength of 59.5 MPa after being heated to 800℃.

[0067] The prepared geopolymer pulp has a compressive strength of 87.8 MPa after being heated to 1000℃.

[0068] In the example s c,T / s c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0069] In the example e c,T / e c The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the calcination temperature.

[0070] In the example E 0,T / E 0 The correlation model between the value and temperature is as follows: in , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the calcination temperature.

[0071] Example of a geopolymer stress-strain model: in , which is a parameter describing the shape of the rising segment of the curve. These represent the compressive strength, peak strain, and elastic modulus of the geopolymer after high temperature. The fitting coefficients are denoted as .

[0072] Table 7 In Example 4 Value table Table 8 In Example 4 Value table In all embodiments, the compressive strength, elastic modulus, and peak strain exhibit significant abrupt changes at 1000℃. As temperature increases, the linearity of the stress-strain curves gradually strengthens before and after the peak strain. Figure 1 to Figure 3 It can be seen that the model's predictions of compressive strength, peak strain, and elastic modulus for each embodiment agree well with the measured values, with prediction errors all controlled within ±15%. Figure 4 As can be seen, the stress-strain relationship curve predicted by the model is basically consistent with the measured curve in the rising segment. Although there is some deviation in the falling segment, the overall trend is still quite consistent, and the error is within an acceptable range. The above results indicate that the model has high prediction accuracy and good applicability.

[0073] The above description is merely a preferred embodiment of the present invention, but the present invention is not limited to the specific embodiments described above. Those skilled in the art can make various modifications, additions, or substitutes using similar methods without departing from the principles of the present invention, and these should also be considered within the scope of protection of the present invention. However, the possibility of using other terms is not excluded. These terms are used merely for the convenience of describing and explaining the essence of the present invention, and interpreting them as any kind of additional limitation would contradict the spirit of the present invention.

Claims

1. A temperature-related stress-strain prediction model for high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete, characterized in that, include: The compressive strength prediction model is used to output the predicted compressive strength after high temperature at the target calcination temperature T. σ c,T ; The peak strain prediction model is used to output the predicted peak strain value after high temperature at the target calcination temperature T. ε c,T ; The elastic modulus prediction model is used to output the predicted elastic modulus value after high temperature at the target calcination temperature T. E 0,T ; Stress-strain full curve generation model, used to generate predicted values σ c,T , ε c,T and E 0,T The stress-strain curve at the target calcination temperature T is generated by using a rational fractional piecewise function.

2. The temperature-related stress-strain prediction model according to claim 1, characterized in that, The compressive strength prediction model adopts the following form: ； in: σ c Compressive strength at room temperature; , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the target calcination temperature T; a, b, and c are fitting parameters.

3. The temperature-related stress-strain prediction model according to claim 1, characterized in that, The peak strain prediction model adopts the following form: ； in: ε c Peak strain at room temperature; , They represent ( T -20) / 1000、( T -400) / 1000 is a quantity related to the target calcination temperature T.

4. The temperature-related stress-strain prediction model according to claim 1, characterized in that, The elastic modulus prediction model adopts the following form: ； in: E 0 The elastic modulus at room temperature; , They represent ( T -20) / 1000、( T -600) / 1000 is a quantity related to the target calcination temperature T.

5. The temperature-related stress-strain prediction model according to claim 1, characterized in that, The stress-strain full curve generation model adopts the following form: ； in: σ This represents the stress value. ε This is the strain value; , which is a parameter describing the shape of the rising segment of the curve; The fitting coefficients are denoted as .

6. The temperature-related stress-strain prediction model according to claim 1, characterized in that, The multi-scale fiber-hybrid geopolymer concrete comprises a geopolymer precursor, refractory aggregate, alkali activator, water, and multi-scale hybrid fibers; the multi-scale hybrid fibers comprise at least two of wollastonite fibers, basalt fibers, and steel fibers; the geopolymer precursor comprises fly ash and / or metakaolin; and the refractory aggregate is ceramic aggregate.

7. A method for constructing a temperature-related stress-strain prediction model as described in claim 1, characterized in that, Includes the following steps: Multiple sets of high-temperature reinforced multi-scale fiber-hybrid geopolymer concrete specimens were prepared, and their compressive strength, peak strain, and elastic modulus were tested at room temperature and at several high-temperature target calcination temperatures. Based on the performance at room temperature, the compressive strength, peak strain and elastic modulus at the calcination temperature of each high-temperature target were normalized. Regression analysis was performed on the normalized compressive strength data and temperature to construct a compressive strength prediction model; Regression analysis was performed on the normalized peak strain data and temperature to construct a peak strain prediction model. Regression analysis was performed on the normalized elastic modulus data and temperature to construct an elastic modulus prediction model. Based on the output parameters of the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model, and combined with rational fractional piecewise functions, a temperature-related stress-strain full curve generation model is constructed.

8. A method for predicting the high-temperature mechanical properties of high-temperature reinforced multi-scale fiber-reinforced hybrid geopolymer concrete, characterized in that, The temperature-related stress-strain prediction model as described in claim 1 includes the following steps: Obtain the ambient temperature axial compressive mechanical parameters of the geopolymer concrete to be predicted, including its ambient temperature compressive strength. σ c Peak strain at room temperature ε c and room temperature elastic modulus E 0 ; By calling the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model, and inputting the target calcination temperature T and room temperature axial compressive parameters, the compressive strength prediction model, peak strain prediction model, and elastic modulus prediction model are obtained respectively. σ c,T , ε c,T and E 0,T ; Call the stress-strain full curve generation model and input... σ c,T , ε c,T and E 0,T Generate the full stress-strain curve at the target calcination temperature T; The output shows the predicted results of compressive strength, peak strain, elastic modulus, and stress-strain curve at the target calcination temperature T.

9. The prediction method according to claim 8, characterized in that, The prediction model covers the entire temperature range from room temperature to 1000℃, and the relative error of the prediction results is controlled within ±15%.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the function of the temperature-related stress-strain prediction model as described in claim 1, or implements the steps of the construction method as described in claim 7, or implements the steps of the prediction method as described in claim 8.

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